The modern manufacturing facility is making increasing use of computers, microprocessors and other machine-based "intelligence" for the purpose of producing articles of uniform high quality. Herein, the machine processing an article will be referred to as the "processing machine" and the article undergoing such processing will be referred to as the "workpiece." The portion of the processing machine physically interacting with the workpiece will be denoted as the "tool" understanding thereby that the tool may be a mechanical cutting, drilling or shaping implement, laser, water jet or any other device, implement, or form of energy interacting with the workpiece and causing changes therein.
The computer control of the processing machine may take the form of a microprocessor or computer embedded within the particular processing machine and dedicated to the control of that single machine. Computer control may also take the form of a detached mini-, midi-, personal, or mainframe computer, physically separate from the processing machine but electronically connected (wired or wireless) thereto and controlling the machine's processing of the workpiece. A computer may thus control one or more processing machines and may be physically remote from the processing machine, perhaps by many miles utilizing intranet, internet or other modern data transmission technology.
For the purposes of illustration, the present invention will be described in terms of the common case in which the controlling computer is embedded within the processing machine and dedicated to the control of just that machine. However, the present invention is not so limited and numerous particular embodiments of computer control are included within its scope, as would be obvious to those having ordinary skills in the art.
Computer-Numerical-Control "CNC" is the designation for the common machining technique whereby the workpiece and the tool are positioned, oriented and moved through space according to trajectories determined by instructions stored in a computer or microprocessor. In full generality, three variables determine the position of the tool relative to the workpiece in space at any given instant of time while three more variables determine the instantaneous orientation of the tool relative to the workpiece. Thus, the full control of a workpiece and tool would require the specification of 6 variables as functions of time, determining thereby the trajectories of workpiece and tool and the orientations thereof as each traverses its designated trajectory. Control variables in addition to location and orientation may be required to specify precisely the processing of the workpiece. For example, in laser processing additional commands may be issued by the controlling computer to determine beam power, beam on or off, continuous or pulsed. In practice, CNC machines would control several types of motion and orientation of the workpiece and tool but would typically lack the full flexibility to control every parameter in the processing of the workpiece. Although CNC or computer control of a processing machine, is referenced herein, it is not intended thereby to limit or to exclude any particular form of computer control of orientation, location, trajectory or other processing parameters.
The use herein of "tuning" of the control system or control loop refers to the adjustment of parameters in the control loop to achieve the desired performance of the processing machine. The systems for controlling the workpiece and/or tool during processing must meet several criteria to be effective and robust, producing high quality results in practical production environments. One important criterion for the control system is that it be stable in response to disturbances which may be introduced into the production process in an uncontrolled, random and unpredictable manner. Such disturbances may result from random fluctuations in the torque generated by motors driving the machine, torque ripple, variations in materials properties of the workpiece, random noise in the electronic or mechanical systems, vibrations external to the machine, and many other possible disturbances well known in the art. An unstable control system will not cause the machining process to return to its desired state when such a disturbance is encountered. An unstable system will run as far as the machine allows in a particular direction, oscillate with increasing amplitude or oscillate with a non-decreasing amplitude in response to such a disturbance. Thus, absence of instability, or stability, is one condition necessary for practical operation of a control system.
Improperly tuned machines may affect the quality of the workpiece in one or more undesirable ways. Unstable systems are clearly unacceptable in that any slight disturbance to the processing of the workpiece will typically lead to large processing errors. However, the control system must also be tuned to have adequate margins of stability in order to achieve good quality processing under all reasonable working conditions. That is, the control system must not only be stable but also remain stable when characteristics of the machine change over time during operation. Therefore, it is necessary that the control system remain stable as machine components wear, frictional forces may change over time and/or inertia of various machine components may change.
In addition to being stable with adequate margins of stability, the control system needs to reject disturbances sufficiently strongly such that any perturbations reaching the tool-workpiece interface will be too small, and endure for too short a time period, to affect the quality of the final workpiece. Thus, good stability, margin of stability and disturbance rejection are among the characteristics of a properly functioning machine control system. Achieving these criteria in a practical production environment is one purpose of the present invention.
Several problems may arise for improperly tuned machines even though the control system is stable. For example, variations in the torque output of drive motors, "ripples," invariably present in practical motors will affect the surface finish of the workpiece if the control system too lightly damps such disturbances. Additionally, commands from the typical CNC device for controlling the motion of tool and/or workpiece may overshoot in velocity, position or both, resulting in improperly processed parts. Such commands may result in oscillations and cause imperfections in the workpiece beyond the range of acceptability.
In some cases, improper tuning may even result in audible "squeals" being produced by the machine during processing, resulting in a perception of poor quality and perhaps rapid wearing of the machine components. These are a few of the important criteria to be achieved when a machine control loop is adequately tuned. Other criteria are discussed elsewhere herein.
There are many approaches to control loop tuning. In general, there are two broad classifications control loop tuning. In time domain tuning, the time response of the system to certain inputs is measured. Frequently, an abrupt "step" input is provided and the response of the machine with time then determined. Other inputs may be employed within the scope of time domain tuning.
An alternative but mathematically equivalent procedure for analyzing control systems is to make use of the frequency domain, related to the time domain by the Laplace transform. A linear differential equation describing the time behavior of a system (time domain) may be replaced by an equivalent set of algebraic equations in the frequency domain by applying the Laplace transform to all terms of the differential equation. The resulting algebraic equations are typically more easily solved than the time domain differential equations and time domain solutions derived (if necessary) by applying inverse Laplace transform to the solution(s) of the algebraic equations. Also, the Laplace transform may be applied making use of a complex frequency variable, resulting in a description of the system in the complex frequency plane. Complex frequency introduces additional mathematical tools that may be applied in the complex plane for further analysis of the system.
In one embodiment, the present invention makes use of an analysis of the control system in the frequency domain, typically in the range from 0 (dc) to approximately 1,000 Hertz (1 KHz). The response of the system in both magnitude and phase is determined as functions of inputs of various frequencies, most conveniently supplied by means of random noise driving signals containing therein a spectrum of frequencies. Both velocity and position responses are considered. In this embodiment, the system makes use of a direct measurement of the frequency response function ("FRF"), also known as a Bode plot. However, Bode plot signifies to some the use of a mathematical description of the system, necessarily only an approximation to the real machine. This embodiment of the present invention is not dependent on the use of mathematical model or approximation to the system in order to derive the tuning parameters. Rather, it makes use of a directly measured FRF from which the tuning of the system is then derived. Thus, the term "FRF" is used herein.
In one aspect, the present invention relates to tuning a machine tool without introducing a mathematical model of the dynamical behavior of the machine; necessarily an approximation that would have to be re-done from machine to machine. In another aspect, the invention relates to selection of worst-case FRF's (or nearly so) to insure that practical operation of the machine under any feasible conditions will not result in an improperly tuned machine. In an additional aspect, the present invention relates to combining piecewise- FRF data to construct a composite FRF which is used to achieve good tuning parameters. Software tools are described herein as convenient means for performing this composition.
As described more fully elsewhere herein, tuning of a control loop pursuant to the procedures of the present invention is not limited to adjustment of particular electronic or computer components which may be present in the control loop of some machines but not others. The present invention, in one embodiment, provides methods for tuning general control systems by a four step process: 1) Measuring the performance of the system under specified excitations with control loop parameters set at any convenient values (subject to general procedures described in detail elsewhere); 2) Computationally deconvoluting the measured behavior of the system such that the particular parameters under which measurements were made are extracted from the measured behavior, permitting; 3) New parameters to be introduced computationally to determine the effect on the control system of new parameters without further tests involving the processing machine; 4) Testing the processing machine with the computationally-determined tuning parameters. Thus, a correctly tuned machine may be obtained in most cases with extraction of measured data, off-line processing of that data and adjustments of the tuning parameters as determined by the off-line computation. Typically, one such adjustment results in an adequately tuned machine, but the above process can be repeated if additional tuning is required, and/or if periodic tuning is desired.
Thus, one embodiment of the present invention can make use of direct measurement of the frequency response function ("FRF") of the machine to determine the proper tuning parameters. This embodiment does not use an assumed mathematical model of the behavior of the machine and thereby does not introduce the assumptions and simplifications inherent in any mathematical modeling of a real machine.
The description herein will make use of the common Laplace transform notation of control engineering relating continuous time to continuous frequency (complex frequency, in its most general form). However, as digital electronics comes to dominate control engineering, it is known that the Laplace transform can be replaced by the z-transform that relates properties at discrete time intervals to frequency. There is no essential difference in the practice of this invention an analogue form or digital form.
The present invention therefore relates to a method of tuning comprising a composite set of various tuning techniques. The present invention is directed to tuning velocity loops for machine tool under circumstances that the tuning will be stable, have adequate margins of stability and generally provide robust control with ample rejection of disturbances under all plausible operating conditions. Thus, the present tuning method also relates to obtaining various operating conditions of the machine and selecting what are generally worst plausible scenarios under each circumstance. The resultant tuning is a composite of various tuning techniques obtained under various operating conditions resulting in good tuning throughout the operating range. In contrast to prior art tuning methods and apparatus, the tuning methods and apparatus of one aspect of the present invention presume no special components being present in the control or mechanical system, make use of random noise excitations to generate numerous frequency response functions, and mathematically deconvolute the measured machine performance without the need for a mathematical (e.g. differential equation) model for the performance of the system with the attendant uncertainty and arbitrariness of such a model.